Warning, the protected name Chi has been redefined and unprotected
             There all together, 2, different equivalence classes

For the equivalence class of patterns, {

    {[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2]},

    {[1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]}}

the member , {[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2]},

    has a scheme of depth , 4

                                  here it is:

[[[], {}, {}], [[1], {[1, 1], [0, 2]}, {}],

    [[1, 1], {[1, 1, 0], [0, 2, 0], [1, 0, 1], [0, 1, 1], [0, 0, 2]}, {1, 2}],

    [[1, 2], {[1, 1, 0], [0, 2, 0], [0, 1, 1]}, {1, 2}],

    [[2, 1], {[0, 2, 0], [0, 1, 1]}, {}],

    [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2],

    {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 2, 3}],

    [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}],

    [[2, 1, 1], {[0, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3}],

    [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}],

    [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1],

    {[0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]},

    {1, 2, 3}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}],

    [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1],

    {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 2, 0], [0, 0, 1, 1, 1]},

    {3, 4}]]

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                         [1, 2, 1, 1, 1, 1, 1, 1, 1, 1]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                         [1, 6, 1, 1, 1, 1, 1, 1, 1, 1]

 Using  the scheme, the first, , 10, terms for , 3,  copies of each letter are

                        [1, 20, 1, 1, 1, 1, 1, 1, 1, 1]

For the equivalence class of patterns, {

    {[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 2, 1]},

    {[1, 2, 3], [1, 3, 2], [2, 1, 3], [3, 1, 2], [3, 2, 1]},

    {[1, 2, 3], [1, 3, 2], [2, 3, 1], [3, 1, 2], [3, 2, 1]},

    {[1, 2, 3], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]}}

the member , {[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 2, 1]},

    has a scheme of depth , 4

                                  here it is:

[[[], {}, {}], [[1], {[1, 1], [0, 2], [3, 0]}, {}],

    [[1, 2], {[1, 1, 0], [0, 2, 0], [0, 1, 1]}, {1, 2}], [[1, 1],

    {[3, 0, 0], [1, 1, 0], [0, 2, 0], [1, 0, 1], [0, 1, 1], [0, 0, 2]}, {1, 2}]

    , [[2, 1], {[0, 3, 0], [1, 1, 0], [0, 1, 1]}, {}], [[2, 1, 2],

    {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 2, 3}], [

    [2, 1, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 3, 0], [1, 0, 1, 0]}, {2, 3}

    ], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}],

    [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}],

    [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}],

    [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], {

    [0, 1, 0, 1, 1], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0],

    [0, 1, 0, 2, 0]}, {3, 4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}],

    [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}]]

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                         [1, 2, 1, 0, 0, 0, 0, 0, 0, 0]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                         [1, 6, 1, 0, 0, 0, 0, 0, 0, 0]

 Using  the scheme, the first, , 10, terms for , 3,  copies of each letter are

                        [1, 20, 1, 0, 0, 0, 0, 0, 0, 0]

                         Out of a total of , 2, cases

                      2, were successful and , 0, failed

                               Success Rate: , 1.

                             Here are the failures

                                       {}